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The Game Theory of College Rankings

Source: http://www.columbiaspectator.com/2010/09/20/game-theory-college-rankings

Every year, the US News and World Report posts their annual college and university rankings. Students, faculty, and administrators of these schools, as well as prospective students and their parents, look forward to seeing the new rankings every year. High-achieving students often want to attend a top 20, top 10, or even #1 university. Due to the greater emphasis being put on rankings in the past years, many schools have added it to their mission statements to be a top ranked university and many are actively seeking to improve their ranking. This seems like a good idea, as keeping colleges competitive and wanting to be the best in the country will only improve the academic quality of these schools, right?

Not necessarily. The US News and World Report has published the methodology of their rankings, and this is what has schools actively seeking to better their ranking. The thing is, they are making small changes that won’t necessarily better their school at all, but will boost them in the rankings. For example, 15% of the rankings is student selectivity (i.e. cutting off admission for students that have below a certain SAT/ACT score or who are not in the top 10% of their class). Thus, some colleges who may have previously been accepting those who were exceptions to the 10% rule (maybe they were in the top 15% but had an overall great application) are now strictly cutting it off at 10%. This will better their ranking, but won’t necessarily help them to become a better school. The same goes for their class size criteria: the greater percentage of classes that the school offers that are capped at 20 students, the greater the schools ranking will be. Some colleges are simply allowing 19 or 20 students in their classes rather than 22 or 23, like they had been, just to improve their rankings. These changes are providing a competitive environment between schools as well as a moral dilemma for those schools that only want to make changes for the good of the school, not just the good of the rankings.

This provides somewhat of a “prisoner’s dilemma”. In this classic game theoretic problem, there are two prisoners who can either confess to their crime or not confess. They are making this decision individually, without discussing it with each other, and are told that if they confess and their partner doesn’t confess, they will get away with no jail time while their partner will get 10 years. When being told that, each prisoner is likely going to want to confess. However, if both prisoners are using that mindset, they will both confess and if these happens, they will split the jail time. However, if neither of them confess, they will both be charged for a lesser crime and spend only 1 year in jail each. So, if only they cooperated, they would receive a much better outcome. However, they will each confess, receiving 4 years in jail each despite it not being the best outcome.

Similarly to this dilemma, consider two schools: College 1 and College 2. If College 1 makes policy changes to better their rankings, but College 2 does not, College 1 will receive a positive payoff and College 2 will receive a payoff of 0, and vice versa. If both College 1 and 2 chose not to make any changes for rankings, they would each receive a positive payoff, which would actually be the best outcome for each college. However, since each college will assume the other college is going to try to increase their rankings, they will both manipulate their policy and administrative changes in order to remain competitors to the other colleges. So, similarly to the prisoner’s dilemma, even though it would be the most beneficial for both colleges to resist changes for rankings, neither college will trust that the other will actually resist, and so they both will jockey for position in the rankings, receiving smaller, but still positive, payoffs. This application of game theory in the real world is a great example as it shows how it is not only your strategy and your decision that matters, but also the strategies and decisions of the other “players”.

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